Question

P and S waves from an earthquake travel at different speeds, and this difference helps locate the earthquake "epicenter" (where the disturbance took place).

a. assuming typical speeds of 8.5 km/s and 5.5 km/s for P and S waves respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 1.7 min apart?
b. Is one seismic station sufficient to determine the position of the epicenter? Explain.

Answer 1

a) The earthquake occurred at a distance of 1589.5 km

b) No, one seismic station is not sufficient to determine the position of the epicenter

Step-by-step explanation:

Speed of wave P,
`v_(p) = 8.5 km/s` = 8500 m/s

Speed of wave S,
`v_(s) = 5.5 km/s` = 5500 m/s

Difference in arrival time of the two waves, Δt =
`t_(s) - t_(p)`

Where
`t_(s)` is the arrival time for wave S, and
`t_(p)` is the arrival time for wave P

`Speed = (Distance)/(time) \\time = (Distance)/(speed)`

The two waves cover the same distance, d

`t_(p) = (d)/(v_(p) ) \\t_(s) = (d)/(v_(s) )\\`

Δt =
`(d)/(v_(s) ) - (d)/(v_(p) )`

Δt =
`d((1)/(v_(s) ) -(1)/(v_(p) ) )`

Δt =
`d((v_(p)-v_(s) )/(v_(s) v_(p) ))`

d = Δt
`((v_(s)v_(p) )/(v_(p)-v_(s) ) )`

d =
`102((8500*5500)/(8500-5500))`

d = 1589500 m

d = 1589.5 km

b) To determine the location of an earthquake, the distance of the earthquake must be determined from at least three seismic stations. Circles with the appropriate radius are then drawn around each station. The intersection of the three circles determines the epicenter of the earthquake.